Question

1. Tìm x, biết:
a) x³ - 24 = x
b) x² - 1 = 2(x+1)

Answer 1

a, \(x^3-24=x\)

<=> \(x^3-x-24=0\)

<=>\(x^3-3x^2+3x^2-9x+8x-24=0\)

<=> \(x^2\left(x-3\right)+3x\left(x-3\right)+8\left(x-3\right)=0\)

<=> \(\left(x^2+3x+8\right)\left(x-3\right)=0\)

<=> \(\left(x^2+2.\frac{3}{2}x+\frac{9}{4}+\frac{23}{4}\right)\left(x-3\right)=0\)

<=>\(\left[\left(x+\frac{3}{2}\right)^2+\frac{23}{4}\right]\left(x-3\right)=0\)

=> x-3=0 ( \(do\left(x+\frac{3}{2}\right)^2+\frac{23}{4}>0\))

<=> x=3

b, \(x^2-1=2\left(x+1\right)\)

<=> \(\left(x-1\right)\left(x+1\right)-2\left(x+1\right)=0\)

<=> \(\left(x+1\right)\left(x-3\right)=0\) => x=-1 hoặc x=3